Magnetism and Magnetic Materials Covering basic physical concepts, experimental methods, and applications, this book is an indispensable text on the fascinating science of magnetism, and an invaluable source of practical reference data. Accessible, authoritative, and assuming undergraduate familiarity with vectors, electromagnetism and quantum mechanics, this textbook is well suited to graduate courses. Emphasis is placed on practical calculations and numerical magnitudes from nanoscale to astronomical scale focussing on modern applications, including permanent magnet structures and spin electronic devices. Each self-contained chapter begins with a summary, and ends with exercises and further reading. The book is thoroughly illustrated with over 600 figures to help convey concepts and clearly explain ideas. Easily digestible tables and data sheets provide a wealth of useful information on magnetic properties. The 38 principal magnetic materials, and many more related compounds, are treated in detail. leads the Magnetism and Spin Electronics group at Trinity College, Dublin, where he is Erasmus Smith s Professor of Natural and Experimental Philosophy. An authority on magnetism and its applications, he has been awarded the Gold Medal of the Royal Irish Academy and the Charles Chree Medal of the Institute of Physics for his work on magnetic materials.
Magnetism and Magnetic Materials J. M. D. COEY Trinity College, Dublin
University Printing House, CambridgeiCB2i8BS,iUnited Kingdom Cambridge University Press is part of the University of Cambridge. It furthers the University s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. Information on this title: /9780521816144 C 2010 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2010 5th printing 2015 Printed in the United Kingdom by TJ International Ltd, Padstow, Cornwall A catalogue record for this publication is available from the British Library ISBN 978-0-521-81614-4 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
Contents List of tables of numerical data Preface Acknowledgements ix xi xiii 1 Introduction 1 1.1 A brief history of magnetism 1 1.2 Magnetism and hysteresis 7 1.3 Magnet applications 13 1.4 Magnetism, the felicitous science 19 2 Magnetostatics 24 2.1 The magnetic dipole moment 24 2.2 Magnetic fields 28 2.3 Maxwell s equations 41 2.4 Magnetic field calculations 43 2.5 Magnetostatic energy and forces 50 3 Magnetism of electrons 62 3.1 Orbital and spin moments 63 3.2 Magnetic field effects 74 3.3 Theory of electronic magnetism 87 3.4 Magnetism of electrons in solids 92 4 Magnetism of localized electrons on the atom 97 4.1 The hydrogenic atom and angular momentum 97 4.2 The many-electron atom 100 4.3 Paramagnetism 106 4.4 Ions in solids; crystal-field interactions 114 5 Ferromagnetism and exchange 128 5.1 Mean field theory 129 5.2 Exchange interactions 135 5.3 Band magnetism 144 5.4 Collective excitations 161
vi Contents 5.5 Anisotropy 168 5.6 Ferromagnetic phenomena 174 6 Antiferromagnetism and other magnetic order 195 6.1 Molecular field theory of antiferromagnetism 196 6.2 Ferrimagnets 200 6.3 Frustration 203 6.4 Amorphous magnets 209 6.5 Spin glasses 218 6.6 Magnetic models 221 7 Micromagnetism, domains and hysteresis 231 7.1 Micromagnetic energy 234 7.2 Domain theory 239 7.3 Reversal, pinning and nucleation 244 8 Nanoscale magnetism 264 8.1 Characteristic length scales 265 8.2 Thin films 267 8.3 Thin-film heterostructures 274 8.4 Wires and needles 293 8.5 Small particles 295 8.6 Bulk nanostructures 299 9 Magnetic resonance 305 9.1 Electron paramagnetic resonance 307 9.2 Ferromagnetic resonance 313 9.3 Nuclear magnetic resonance 318 9.4 Other methods 329 10 Experimental methods 333 10.1 Materials growth 333 10.2 Magnetic fields 340 10.3 Atomic-scale magnetism 343 10.4 Domain-scale measurements 353 10.5 Bulk magnetization measurements 360 10.6 Excitations 368 10.7 Numerical methods 370 11 Magnetic materials 374 11.1 Introduction 374 11.2 Iron group metals and alloys 384
vii Contents 11.3 Rare-earth metals and intermetallic compounds 398 11.4 Interstitial compounds 407 11.5 Oxides with ferromagnetic interactions 410 11.6 Oxides with antiferromagnetic interactions 417 11.7 Miscellaneous materials 432 12 Applications of soft magnets 439 12.1 Losses 441 12.2 Soft magnetic materials 448 12.3 Static applications 453 12.4 Low-frequency applications 454 12.5 High-frequency applications 457 13 Applications of hard magnets 464 13.1 Magnetic circuits 466 13.2 Permanent magnet materials 469 13.3 Static applications 473 13.4 Dynamic applications with mechanical recoil 481 13.5 Dynamic applications with active recoil 485 13.6 Magnetic microsystems 491 14 Spin electronics and magnetic recording 494 14.1 Spin-polarized currents 497 14.2 Materials for spin electronics 515 14.3 Magnetic sensors 516 14.4 Magnetic memory 522 14.5 Other topics 525 14.6 Magnetic recording 530 15 Special topics 542 15.1 Magnetic liquids 543 15.2 Magnetoelectrochemistry 547 15.3 Magnetic levitation 549 15.4 Magnetism in biology and medicine 555 15.5 Planetary and cosmic magnetism 565 Appendices 580 Appendix A Notation 580 Appendix B Units and dimensions 590 Appendix C Vector and trigonometric relations 595 Appendix D Demagnetizing factors for ellipsoids of revolution 596
viii Contents Appendix E Field, magnetization and susceptibility 597 Appendix F Quantum mechanical operators 598 Appendix G Reduced magnetization of ferromagnets 598 Appendix H Crystal field and anisotropy 599 Appendix I Magnetic point groups 600 Formula index 601 Index 604
List of tables of numerical data Unit conversions rear endpaper Physical constants rear endpaper The magnetic periodic table front endpaper Demagnetizing factors 596 Diamagnetic susceptibilities of ion cores 76 Properties of the free-electron gas 79 Susceptibilities of diamagnetic and paramagnetic materials 87 Spin-orbit coupling constants 105 Properties of 4f ions 114,125 Properties of 3d ions 115 Susceptibility of metals 134 Kondo temperatures 146 Intrinsic magnetic properties of Fe, Co, Ni 150 Energy contributions in a ferromagnet 179 Faraday and Kerr rotation 190,191 Reduced magnetization; Brillouin theory 598 Model critical exponents 224 Domain wall parameters for ferromagnets 242 Micromagnetic length scales for ferromagnets 266 Antiferromagnets for exchange bias 278 g-factors for ferromagnets 314 Magnetism of elementary particles 319 Nuclei for NMR 320 Nuclei for Mössbauer effect 330 Nuclear and magnetic scattering lengths for neutrons 347 Properties of selected magnetic materials 375 Magnetic parameters of useful magnetic materials 377 Metallic radii of elements 379 Ionic radii of ions 380 Soft materials for low-frequency applications 450 Soft materials for high-frequency applications 452 Properties of permanent magnets 471,473 Mean free paths and spin diffusion lengths 499 Properties of materials used for spin electronics 516 Properties of commercial ferrofluids and microbeads 547
Preface This book offers a broad introduction to magnetism and its applications, designed for graduate students and advanced undergraduates as well as practising scientists and engineers. The approach is descriptive and quantitative, treating concepts, phenomena, materials and devices in a way that emphasises numerical magnitudes, and provides a wealth of useful data. Magnetism is a venerable subject, which underwent four revolutionary changes in the course of the twentieth century understanding of the physics, extension to high frequencies, the avalanche of consumer applications and, most recently, the emergence of spin electronics. The reader probably owns one or two hundred magnets, or some billions if you have a computer where each bit on the hard disc counts as an individually addressable magnet. Sixty years ago, the number would have been at best two or three. Magnetics, in partnership with semiconductors, has created the information revolution, which in turn has given birth to new ways to research the subject numerical simulation of physical theory, automatic data acquisition and web-based literature searches. The text is structured in five parts. First, there is a short overview of the field. Then come eight chapters devoted to concepts and principles. Two parts follow which treat experimental methods and materials, respectively. Finally there are four chapters on applications. An elementary knowledge of electromagnetism and quantum mechanics is needed for the second part. Each chapter ends with a short bibliography of secondary literature, and some exercises. SI units are used throughout, to avoid confusion and promote magnetic numeracy. A detailed conversion table for cgs units, which are still in widespread use, is provided inside the back cover. There is some attempt to place the study of magnetism in a global context; our activity is not only intellectual and practical, it is also social and economic. The text has grown out of courses given to undergraduates, postgraduates and engineers over the past 15 years in Dublin, San Diego, Tallahassee, Strasbourg and Seagate, as well as from the activities of our own research group at Trinity College, Dublin. I am very grateful to many students, past and present, who contributed to the venture, as well as to numerous colleagues who took the trouble to read a chapter and let me have their criticism and advice, and correct at least some of the mistakes. I should mention particularly Sara McMurry, Plamen Stamenov and Munuswamy Venkatesan, as well as Grainne Costigan, Graham Green, Ma Qinli and Chen Junyang, who all
xii Preface worked on the figures, and Emer Brady who helped me get the whole text into shape. Outlines of the solutions to the odd-numbered exercises are available at the Cambridge website /9780521816144. Comments, corrections and suggestions for improvements of the text are very welcome; please post them at www.tcd.ie/physics/magnetism/coeybook.php. Finally, I am grateful to Wong May, thinking of everything we missed doing together when I was too busy with this. Dublin, November 2009
Acknowledgements The following figures are reproduced with permission from the publishers: American Association for the Advancement of Science: 14.18, p.525 (margin), p.537 (margin),14.27; American Institute of Physics: 5.25, 5.31, 6.18, 8.5, 8.33, 10.12, 11.8; American Physical Society: 4.9, 5.35, 5.40, 6.27a, 6.27b, 8.3, 8.8, 8.9, 8.15, 8.17, 8.18, 8.21, 8.22, 8.26, 8.29, 9.5, p.360 (margin), 11.15, 14.16; American Geophysical Union p.572 (margin); United States Geological Survey Geomagnetism Program: 15.18, p.572 (margin); American Society for Metals: 5.35; Cambridge University Press: 4.15, 4.17, 7.8, 7.18, 9.12, 10.16, p.573 (margin); Elsevier: 6.23, 8.2, 8.4, 11.22, 14.22, 14.23, 14.26, 15.22; Institute of Electrical and Electronics Engineers: 5.32, 8.31, 8.34, 8.35, 9.6, 11.6, 11.7; MacMillan Publishers: 14.17, 15.4c; Oxford University Press: 5.26; National Academy of Sciences:15.1; Springer Verlag: 4.18, 14.13, 14.21, 15.8, 15.21; Taylor and Francis: 1.6, 2.8b, 10.2; Institution of Engineering and Technology: 11.20; University of Chicago Press: 1.1a; John Wiley: 5.21, 6.4, 6.15, 8.11a,b, 9.9, 12.10 Fermi surfaces are reproduced with kind permission of the University of Florida, Department of Physics, http://www.phys.ufl.edu/fermisurface. Thanks are due to Wiebke Drenckhan and Orphee Cugat for permission to reproduce the cartoons on pages 161 and 531. Figure 15.3 is reproduced by courtesy of Johannes Kluehspiess. Figure 15.5 is reproduced by courtesy of L. Nelemans, High Field Magnet Laboratory, Nijmegen. Figure 15.5 is reproduced by permission of Y. I.Wang, Figure 15.17 is repoduced by courtesy of N. Sadato; Figure 15.23 is reproduced by courtesy of P. Rochette.